Non-classical Metatheory for Non-classical Logics

Non-classical Metatheory for Non-classical Logics

A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical meta-theory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena o...

Truth Values and Connectives in Some Non-Classical Logics

The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...

Labelled non-classical logics

A Uniform Proof Procedure for Classical and Non-Classical Logics

G. Görz & S. Hölldobler, eds. KI-96: Advances in Artificial Intelligence, LNAI 1137, pp. 307–319, c ©Springer Verlag, 1996. Abstract. We present a proof procedure for classical and non-classical logics. The proof search is based on the matrix-characterization of validity where an emphasis on paths and connections avoids redundancies occurring in sequent or tableaux calculi. Our uniform path-che...

On AGM for Non-Classical Logics

The AGM theory of belief revision provides a formal framework to represent the dynamics of epistemic states. In this framework, the beliefs of the agent are usually represented as logical formulas while the change operations are constrained by rationality postulates. In the original proposal, the logic underlying the reasoning was supposed to be supraclassical, among other properties. In this p...